TY - JOUR
T1 - A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm
AU - Zeng , Yuping
AU - Wang , Feng
AU - Weng , Zhifeng
AU - Hu , Hanzhang
JO - Journal of Computational Mathematics
VL - 5
SP - 755
EP - 776
PY - 2021
DA - 2021/08
SN - 39
DO - http://doi.org/10.4208/jcm.2006-m2019-0010
UR - https://global-sci.org/intro/article_detail/jcm/19383.html
KW - Modified weak Galerkin method, A posteriori error estimate, A medius error analysis.
AB - <p style="text-align: justify;">In this paper, we derive a residual based a posteriori error estimator for a modified
weak Galerkin formulation of second order elliptic problems. We prove that the error
estimator used for interior penalty discontinuous Galerkin methods still gives both upper
and lower bounds for the modified weak Galerkin method, though they have essentially
different bilinear forms. More precisely, we prove its reliability and efficiency for the actual
error measured in the standard DG norm. We further provide an improved a priori error
estimate under minimal regularity assumptions on the exact solution. Numerical results
are presented to verify the theoretical analysis.</p>